Heat Engines

Heat EnginesKartavya BholaAdvanced Chemical Engineering thermodynamics

What is a heat engine?Heat Engine is a device used for converting heat energy constantly into mechanical work.

How does a heat engine workIt does this by bringing a working substance from a higher state temperature to a lower state temperatureA heat engine has 3 essential parts:Source or Hot BodySink or Cold bodyWorking Body

The processThe working substance is taken along a cycle of operations. It absorbs heat from source, transforms some part of heat as mechanical energy and remaining part of heat is rejected to sink.Heat energy is never completed completely into work done.

What is a thermodynamic cycleEvery single thermodynamic system exists in a particular state.When a system is taken through a series of different states and finally returned to its initial state, a thermodynamic cycle is said to have occurred. In the process of going through this cycle, the system may perform work on its surroundings, thereby acting as a heat engine.

A generalized thermodynamic cycleA generalized thermodynamic cycle taking place between a hot reservoir at temperature TH and a cold reservoir at temperature TC.The area in red QC is the amount of energy exchanged between the system and the cold reservoir. The area in white W is the amount of work energy exchanged by the system with its surroundings.The amount of heat exchanged with the hot reservoir is the sum of the two.

A generalized thermodynamic cycleIf the system is behaving as an engine, the process moves clockwise around the loop, and moves counter-clockwise if it is behaving as a refrigerator. The efficiency of the cycle is the ratio of the white area (work) divided by the sum of the white and red areas (heat absorbed from the hot reservoir).Any heat engine can be described by its efficiency: the amount of energy input that is actually converted to useful output. Efficiency = Energy out 100% Energy in

Second law of thermodynamics(Kelvin-Planck statement) It is impossible to construct a heat engine operating in a cycle that extracts heat from a reservoir and delivers an equal amount of work.

Means that Qc cannot equal 0 Some Qc must be expelled to the environment Means that e cannot equal 100%

Carnot cycleThe Carnot cycle is a theoretical thermodynamic cycle proposed by Nicolas Lonard Sadi Carnot in 1824 A system undergoing a Carnot cycle is called a Carnot heat engineCarnot cycle1. Reversible isothermal expansion of the gas. During this step the gas is allowed to expand and it does work on the surroundings. The temperature of the gas does not change during the process, and thus the expansion is isothermal. The gas expansion is propelled by absorption of heat energy Q1.We know that for a reversible process dQ=T.dS hence, S1= Q1/T12. Isentropic (reversible adiabatic) expansion of the gas. The gas continues to expand, doing work on the surroundings, and losing an equivalent amount of internal energy. The gas expansion causes it to cool to the "cold" temperature, T2. The entropy remains unchanged.

Carnot cycle3. Reversible isothermal compression of the gas. Now the surroundings do work on the gas, causing an amount of heat energy Q2We know that for a reversible process dQ=T.dS hence, S2= Q1/T1

4. Isentropic compression of the gas (isentropic work input). During this step, the surroundings do work on the gas, increasing its internal energy and compressing it, causing the temperature to rise to T1. The entropy remains unchanged. At this point the gas is in the same state as at the start of step.

Carnot cycle

Work and efficiencyfor a reversible process we may write the amount of work done over a cyclic process as:

Since dU is a state property, its integral over any closed loop is zero and it follows that the area inside the loop on a T-S diagram is equal to the total work performed if the loop is traversed in a clockwise direction, and is equal to the total work done on the system as the loop is traversed in a counterclockwise direction. Total Work Done in a Cyclical Process Equals the Area Inside the Closed Loop on a PV Diagram

Work and efficiency Carnot cycle

From the graph, the amount of entropy gained in process 1 is the same amount of entropy lost in step 3.Evaluation of the above integral for the Carnot cycle. The amount of energy transferred as work is

The total amount of thermal energy transferred from the hot reservoir to the system will be

and the total amount of thermal energy transferred from the system to the cold reservoir will be

The efficiency is defined to be:

Carnots TheoremNo engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between those same reservoirsgives the maximum efficiency possible for any engine using the corresponding temperatures

The efficiency would be 100% if Qc =0.This is only possible if Tc = 0 K (i.e absolute Zero)A temperature of absolute zero cannot be attained.(Third law of thermodynamics)

perfectly reversible engineCONCEPTA device can be operated between same two reservoirs, with same energy transfers (only direction reversed)

perfectly reversible engineCONCEPT

A Reversible Heat Engines has the maximum efficiencyThis is proved by assuming that there is a super heat engine with greater efficiency and showing that it contradicts Carnot's assumption.Consider the case where both the reversible heat engine and the super heat engine remove the same amount of heat energy from the hot reservoir.

If the reversible heat engine delivers work out W and deposits heat Qc = Q - W in the colder reservoir, ThenSuper heat engine does work Ws = W+DW and deposits heat Qcs = Q - W - DW to the cold reservoir.A Reversible Heat Engines has the maximum efficiency

The combined operation of the two engines results in no change Q hot reservoir.Heat energy is taken out of the cold reservoir since the reversible heat engine takes out slightly more than the super heat engine puts in and it shows up as extra work.

This taking heat from a single reservoir and turning it to work with no other changes.Which is a violation of second law of thermodynamics.A Reversible Heat Engines has the maximum efficiencyIt can also be seen from the diagram, that for any cycle operating between temperatures T_H and T_C, none can exceed the efficiency of a Carnot cycle.

All Reversible Heat Engines have same efficiency when operating between the same two temperature reservoirs.Lets assume a heat engine with more efficiency than a perfectly reversible

All Reversible Heat Engines have same efficiency when operating between the same two temperature reservoirs.Heat transferred from cold to hot without outside assistance(forbidden by 2nd law) Second Law Clausius FormIt is impossible to construct a cyclical machine whose sole effect is to transfer energy continuously by heat from one object to another object at a higher temperature without the input of energy by work

SummaryThings we should rememberNo process is possible whose sole result is the absorption of heat from a reservoir and the conversion of this heat into work. [Kelvin-Planck statement of the second law]No process is possible whose sole result is the transfer of heat from a cooler to a hotter body. [Clausius statement of the second law]Heat Engine is a device used for converting heat energy constantly into mechanical work.If the system is behaving as an engine, the process moves clockwise around the loop, and moves counter-clockwise if it is behaving as a refrigerator.The Carnot cycle is a theoretical thermodynamic cycle.Reversible isothermal expansion Isentropic (reversible adiabatic) expansion Reversible isothermal compressionIsentropic (reversible adiabatic) CompressionTotal Work Done in a Cyclical Process Equals the Area Inside the Closed Loop on a PV DiagramPerfectly reversible engine is device can be operated between same two reservoirs, with same energy transfers (Only direction reversed)A Reversible Heat Engines has the maximum efficiencyAll Reversible Heat Engines have same efficiency when operating between the same two temperature reservoirs.

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